Optimal Path-Planning with Random Breakdowns

TL;DR

This paper develops a path-planning model that accounts for random, spatially inhomogeneous breakdowns and repairs, providing optimal policies using a hybrid numerical approach and illustrating results with Martian terrain data.

Contribution

It introduces a novel model for path-planning under random breakdowns using piecewise-deterministic Markov processes and develops an efficient numerical solution method.

Findings

Optimal policies depend on breakdown rate and type.

The numerical method effectively solves complex PDEs.

Application to Martian terrain demonstrates practical relevance.

Abstract

We propose a model for path-planning based on a single performance metric that accurately accounts for the the potential (spatially inhomogeneous) cost of breakdowns and repairs. These random breakdowns (or system faults) happen at a known, spatially inhomogeneous rate. Our model includes breakdowns of two types: total, which halt all movement until an in-place repair is completed, and partial, after which movement continues in a damaged state toward a repair depot. We use the framework of piecewise-deterministic Markov processes to describe the optimal policy for all starting locations. We also introduce an efficient numerical method that uses hybrid value-policy iterations to solve the resulting system of Hamilton-Jacobi-Bellman PDEs. Our method is illustrated through a series of computational experiments that highlight the dependence of optimal policies on the rate and type of breakdowns, with one of them based on Martian terrain data near Jezero Crater.